In the classical case, Peng [1]} proved that the value function
is a viscosity solution of its associated HJB equation. In this section,
we would like to establish the connection between the value function defined in (REF )
and the viscosity solution of HJB equation (REF ) in the setting of the non-Lipschitz generator with delay.
For this, one more assumption is needed, i.e., the generator \(g\)  of BSDE (REF ) is independent of
the second unknown variable \(Z\) . To be specific, throughout Sections 4 and 5, the generator \(g(t, \gamma , y, z, v)=g(t,\gamma , y, v)\)  in BSDE (REF ).
